Rigging a rabbit character
Just an idea more than a real answer, but for that very special case, you should try something like that (sorry for the very quickly done rabbid..) : the trick is to have a ability to have very few points to animate and to be easily able to stay around the wanted shape. 



As you can see, very few vertices :



But all rely on a capsule metaball that I have deformed a bit :


1 : the capsule shown
2 : the capsule drawn as bounding box only




Now the rabbid has some modifiers (from top to bottom) :


Subsurf : because we have few points to animate but want it to stretch smoothly
Shrinkwrap : the most important part here as this modifier allows to stay along the capsule (see below for more explanations)
Solidify : to give it some volume




For the capsule :


Add it : Shift+A then choose 'metaball' and 'capsule' (surely you can also make your own shape instead)
Give it more precision (picture below)
Then convert it to mesh, with Alt+C, then 'mesh from curve'




Now edit it a bit in order to give it the wanted shape (to say it quickly, larger on top, smaller at the base).

We want the rabbid head and face to follow the capsule shape, but not the ears or the eyes. So add a vertex group to the rabbid. Assign this group the head part only and name it 'capsule'. Then, set this vertex group in the shrinkwrap modifier as seen two images above.



Now create your shape keys as you need :



The same kind of thing could be used to allow the eyelids to follow the eyes.